Applying the Jellium Model to Octacarbonyl Metal Complexes ✉ Kun Wang1,2, Chang Xu1, Dan Li1 & Longjiu Cheng 1,2 1234567890():,;

ARTICLE

https://doi.org/10.1038/s42004-020-0285-2 OPEN Applying the Jellium model to octacarbonyl metal complexes ✉ Kun Wang1,2, Chang Xu1, Dan Li1 & Longjiu Cheng 1,2 1234567890():,;

The recently reported octacarbonyl metal complexes M(CO)8 (M = Ca, Sr, Ba) feature interesting bonding structures. In these compounds, the bond order is 7, while accom- modating 8 lone pairs of ligands in forming octa-coordinated complexes or ions. Here, by 2− 2− comparing [Ba(CO)8] and metal clusters of [BaBe8] analogically, we demonstrate that the Jellium model can not only be applied on metal clusters, but is also a useful tool q to understand the electronic structures of [M(CO)8] (M, q = Ca, 2−; Sc, 1−; Ti, 0; V, 1+; Cr, 2+; Ba, 2−). By applying the Jellium model, we ﬁnd that a 20-e model with the conﬁguration 2 6 10 2 |1S |1P |1D |1F | is an appropriate description of the valence bonding structures of M(CO)8 species, where each coordinative bond contains 7/8ths of the bonding orbitals and 1/8th non-bonding orbitals.

1 Department of Chemistry, Anhui University, 230601 Hefei, Anhui, P.R. China. 2 AnHui Province Key Laboratory of Chemistry for Inorganic/Organic Hybrid ✉ Functionalized Materials, 230601 Hefei, Anhui, P.R. China. email: [email protected]

COMMUNICATIONS CHEMISTRY | (2020)3:39 | https://doi.org/10.1038/s42004-020-0285-2 | www.nature.com/commschem 1 ARTICLE COMMUNICATIONS CHEMISTRY | https://doi.org/10.1038/s42004-020-0285-2

he 18-electron rule is a very classic tool for us to understand Here we first compare the molecular orbitals (MOs) of octa- 2− 2− the structures of a large amount of transition metal com- carbonyl metal cations [Ba(CO)8] and metal cluster [BaBe8] T 1 plexes .Especiallyforthehomolepticcarbonylmetal to demonstrate Jellium model is possibly appropriate for under- − − q = complexes, it is very successful to apply Dewar Chatt Duncan- standing the valence bonding orbitals. Then [M(CO)8] (M, q son (DCD) model2 and 18-electron rule to explain the interactions Ca, 2−; Sc, 1−; Ti, 0; V, 1+; Cr, 2+) as the singlet “20e- between carbon monoxide and transition metals, such as the superatom” models are designed and discussed, which are + + + seven-coordinated carbonyl cations [TM(CO)7] (TM = V ,Nb described by Jellium model successfully similar with that of [Ba + + 2− 2− fi 2 6 10 and Ta ) and the eight-coordinated carbonyl cations [TM(CO)8] (CO)8] and [BaBe8] with the con guration of |1S |1P |1D | (TM = Sc+,Y+ and La+)3–5. However, in the recent synthesized 1F2|. Finally, we conclude that each coordinative bond contains 7/ alkaline earth metal complexes M(CO) (M = Ca, Sr and Ba) or 8ths bonding orbitals and 1/8 nonbonding orbitals by applying − − − 8 − anions [TM(CO)8] (TM = Sc ,Y and La ), only the valence bond order analysis. electrons occupying metal−ligand bonding orbitals satisfy the DCD model and the 18-electron rule6,7, including eight degenerate Results and discussion σ → coordinative bonds and two (n − 1)d → π* back- CO TM The similarity of [Ba(CO) ]2− and [BaBe ]2−. Traditionally, donation bonds from alkali earth metal to the ligands8. 8 8 Jellium model is generally applied to explain the stability and There is an interesting inconsistency in understanding the electronic structure of metal cluster14,15, such as the magic sta- electronic structures of octacarbonyl complexes M(CO) (M = − – − − − 8 − bility of the icosahedral Al cluster16 18. The metal cluster can Ca, Sr and Ba) or anions [TM(CO) ] (TM = Sc ,Y and La ) 13 8 be viewed as a superatom, which is comprised from positive on the basis of different chemical bonding theories. It should be charge of atomic nuclei and the innermost electrons, where the noted that all the structures adopt O symmetry. Therefore, on h valence electrons are subjected to an external potential in the basis of valence bond (VB) theory9, there are eight degenerate the delocalized motion as |1S2|1P6|1D102S2|1F142P6|…, where the coordination bonds and two π-backdonation bonds between resulting magic numbers are 2, 8, 20, 40, …. (To distinguish the metal and ligands in M(CO) complexes or ions, where eight 8 electronic shells of atoms, the super shells are depicted as capital carbonyl groups provide eight lone pairs (LPs) of electrons to the letters.) center metal. However, based on the hybrid orbital (HO) the- Therefore, we hypothesize a metal cluster containing eight ory10, only seven empty degenerate orbitals can be provided by coordinative bonds and two d → π* backdonation bonds, such as the d3sp3 hybridized metal. Therefore, the bond orders are [BaBe ]2−, to compare with [Ba(CO) ]2− analogically. Both of inconsistent on the basis of the two classic theories. It is difficult 8 8 the anions strictly satisfy the closed-shell “20e-superatoms” with to arrange the 16 LPs in forming an eight-coordinated complex O symmetry. with the bond order of 7. As for TM(CO) complex or ion, it has h 8 As for the analogical octa-coordinative complex, the O - been hypothesized that the eight σ-type orbitals are contributed h symmetric [BaBe ]2− are optimized at M06-2×/def2tzvpp level of by both the ligands and the transition metal, where the transition 8 theory19,20 in Gaussian 0921 to obtain the singlet electronic metal possibly adopts a higher-level hybridization (such as the f- ground state. The valence electron configuration of [BaBe ]2− is type polarization3) for bonding with the eight carbonyl groups. It 8 a 2t 6t 6a 2e 4 with the HOMO-LUMO gap of 2.77 eV. Based is a reasonable viewpoint to understand the inconsistency of VB 1g 1u 2g 2u g on the Jellium model, the electrons fulfill the ten valence orbitals and HO theories, where the bond orders are both equal to 8. fi 2 6 6 2 4 ’ following the con guration of |1S |1P |1D |1F |1D |, where D Additionally, Zhou s research pointed out that M(CO)8 com- orbitals are split into two groups as (1Dxy,1Dyz and 1Dxz) and plexes or ions have Oh symmetry with the valence electron con- fi 2 6 6 2 2 (1Dx2Ày2 and 1Dz2 ). It should be noticed that the a2u orbital is a guration of a1g t1u t2g a2u eg , where the a2u orbital is explained as the ligand-only orbital, which satisfies the 18-electron rule 1F orbital rather than the 2S orbital, where the energy level of 1F 3,8 fi orbital is in the middle of the two groups of 1D orbitals. perfectly . The electrons in a2u orbital are stabilized by the eld effect of the metal on the ligand cage3,11. Besides the ligand-only Based on the calculation, a2u orbital with f symmetry is shown fi q + + + in Fig. 1. Furthermore, there is a cubic eld in all the M (CO)8 a2u orbital, the other nine MOs (a1g 3t1u 3t2g 2eg) including complexes or ions, which affect the seven-degenerate 1F orbitals seven σ-donation bonds (a1g + 3t1u + 3t2g) and two π- in the coordination, in which the a2u-symmetric 1Fxyz orbital backdonation bonds (2eg) accommodate 18 valence electrons of 8 matches the orbital symmetry in the cubic field of coordination. M(CO)8 complex perfectly , which is also quite reasonable to Therefore, the energy of 1Fxyz orbital is lower than the 2S orbital understand the bonding structures of M(CO)8 complexes or ions. On the basis of the experimental studies, all the ten valence caused by the splitting of F orbitals (Supplementary Fig. 1). The + + + + fi sequences of energy levels of the orbitals are the results of the orbitals (a1g 3t1u 3t2g a2u 2eg) can be ful lled with max- splitting of 1D and 1F orbitals. In the configuration, the number imum 20 electrons for the Oh-symmetric octacarbonyl metal “ ” complexes or ions as singlet state. Therefore, it is attractive for us of valence electrons just equals the magic number 20 achieving magical stability. to understand the state of the ligand-only orbital (a2u orbital) 2− essentially. The comparison of the molecular orbitals of [Ba(CO)8] and 2− 2− For another aspect, the octacarbonyl metal complex or ion is [Ba(Be)8] is shown in Fig. 1. Although [Ba(CO)8] is not a fi 2 with O symmetry, where the octa-coordinative field contributed metal cluster, its con guration can be similarly described as |1S | h 6 6 2 4 1P |1D |1F |1D | based on the Jellium model. Furthermore, a1g, by the positive center metal and eight ligands can be approxi- 2− mately viewed as a homogeneous spherical field or a Jellium t1u and t2g orbitals of [Ba(CO)8] correspond to the 1S, 1P 12,13 orbitals and 1Dxy/1Dyz/1Dxz super orbitals. The eg MOs model . Therefore, we design a series of Oh-symmetric and π q = − − + correspond to the 1D 2À 2 and 1D 2 orbitals as two -type singlet-state [M(CO)8] (M, q Ca, 2 ; Sc, 1 ; Ti, 0; V, 1 ; Cr, x y z 2+; Ba, 2−) complex/ions theoretically to learn their bonding orbitals, which are the two d → π* bonds donated from 5d AOs q structures. Such M (CO)8 complex/ions are 20-e closed-shell of Ba (5dx2Ày2 and 5dz2 AOs) to the 2p AOs of eight CO groups. fi 3 molecules based on the con guration , which exactly satisfy the The ligand-only a2u orbital composed of eight carbonyl groups is magic stability of Jellium model12,13. We are curious that whether also defined as the 1F super orbital based on the diagram in Fig. 1. 2− 2− the ligand-only a2u orbital as a component participate in the eight The similarity of [Ba(CO)8] and [BaBe8] indicates we can fi 2− “ coordinative bonds to form a 20-electron con guration for its understand the valence orbitals of [Ba(CO)8] as a 20e- valence electrons. superatom” based on the Jellium model.

2 COMMUNICATIONS CHEMISTRY | (2020)3:39 | https://doi.org/10.1038/s42004-020-0285-2 | www.nature.com/commschem COMMUNICATIONS CHEMISTRY | https://doi.org/10.1038/s42004-020-0285-2 ARTICLE

2− Fig. 1 The molecular orbitals listed on the basis of the Jellium model. a The molecular orbitals of the singlet [Ba(Be)8] . b The molecular orbitals of the 2− singlet [Ba(CO)8] .

fi 2− For another aspect, we apply MO theory to understand the we do not nd the stable conformation of [Ca(CO)7] , we only σ 2− q → eight -type coordinative bonds in [Ba(CO)8] . There should be calculate the corresponding dissociation energies of M (CO)8 3 3 q + − + 15 MOs contributed by 7 valence AOs of Ba atom (d sp ) and 8 M (CO)7 CO for [Sc(CO)8] , [Ti(CO)8], [V(CO)8] and [Cr σ 2+ AOs of LPs donated from 8 carbonyl groups in forming eight (CO)8] . (The results are listed in Supplementary Table 2.) All q (Ba-C) bonds based on the MO theory. Therefore, the 15 MOs the results indicate that M (CO)8 complex/ions are the should be composed of 7 bonding, 1 nonbonding, and 7 minimums on the PESs. All the O atoms and carbonyl ligands antibonding orbitals fulfilled by 16 electrons successively. In the appear as the same configurations, which include 8 LPs of σ π 15 MOs, the 7 bonding orbitals correspond to the a1g,t1u and t2g electrons localized on O atoms, 8 CO and 16 CO bonds between orbitals. The nonbonding orbital exactly corresponds to the C and O atoms. On the basis of the AdNDP results22, the ligand-only a2u orbital. This is also consistent with the sequence occupancy numbers (|ONs|) of the orbitals of the ligands (in of molecular orbital level energy, where the energy of 1Fxyz orbital Fig. 2a) are very close to the ideal value 2.0|e|, suggesting the as the nonbonding orbital is higher than that of (1Dxy, xz, yz) and reasonable valence properties. lower than the energy of 1Dx2Ày2 and 1Dz2 orbitals. We accomplish the similar MO analysis of Ti(CO)8 with that of 2− [Ba(CO)8] to obtain the similar results. a1g and t1u orbitals q correspond to the 1S and 1P orbitals. t2g orbitals correspond to the The 20-electron model for [M(CO)8] (M, q = Ca, 2−; Sc, 1−; 1D ,1D and 1D orbitals. e orbitals correspond to the 1D 2À 2 Ti, 0; V, 1+; Cr, 2+). To reveal the mystery of the state of the xy yz xz g x y and 1D 2 orbitals, which are the two d → π* bonds donated from ligand-only orbital (a2u orbital), we propose to explain the z q 3d 2À 2 and 3d 2 AOs of Ti to the antibonding π* MOs of bonding structures of [M(CO)8] (M, q = Ca, 2−; Sc, 1−; Ti, 0; x y z V, 1+; Cr, 2+) as the singlet “20e-superatom” models based on carbonyl groups. The ligand-only a2u orbital corresponds to the 1 the comparison in Fig. 1. The typical molecules selected as [Ca F orbital. On the basis of the Jellium model with the configuration 2− − + 2+ 2 6 10 2 (CO)8] , [Sc(CO)8] , Ti(CO)8, [V(CO)8] and [Cr(CO)8] of |1S |1P |1D |1F |, the a2u orbital is not isolated but as a with Oh symmetry are optimized under M06-2×/def2tzvpp the- component in forming the eight coordinative bonds, which can be oretical level to obtain their singlet electronic ground states. All further confirmed by the AdNDP analyses for the coordinative the structures with the coordination information are listed in the bonds of Ti(CO)8. Each Ti-C coordinative bond can be viewed as Supplementary Information (Supplementary Figs. 2−12 and a 9-center-2-electron bond (9c-2e). The AdNDP analysis reveals Supplementary Tables 4−14). All of them have the same valence seven 9c-2e bonds (including one 1S, 3-degenerate 1P, 3- electron configuration of a 2t 6t 6a 2e 4. Each orbital con- degenerate 1D and one 1F super orbitals) correspond to the eight 1g 1u 2g 2u g σ π tributed by both ligand and center metal can be directly bonds. The other two -backdonation bonds (1Dx2Ày2 and 1Dz2 demonstrated by manipulation with structural subunits of Metal- super orbitals) between titanium and the eight ligands can be C bonds, which is confirmed by natural bonding orbital (NBO) viewed as 17c-2e bonds. All the |ONs| are closed to the ideal value q analysis by using the adaptive natural density partitioning of 2.0|e| in Table 1. We deal with the other four [M(CO)8] ions (AdNDP) method22. The AdNDP analyses are shown in Fig. 2a. (M, q = Ca, 2−; Sc, 1−;V,1+; Cr, 2+) in the exactly same fi 2 6 10 2 As for Ti(CO)8 (Fig. 2a), the HOMO-LUMO gap of Ti(CO)8 is pathway to obtain the same con guration of |1S |1P |1D |1F | 5.47 eV under the same theoretical level of M062x/def2tzvpp. As based on the Jellium model and similar results based on the 2− − + 2+ for [Ca(CO)8] , [Sc(CO)8] , [V(CO)8] and [Cr(CO)8] , the AdNDP method. HOMO-LUMO gaps are 3.12, 4.28, 6.94 and 9.12 eV, respectively. As for the a2u orbital in Ti(CO)8, it is a special 9c-2e bond in fi q There are no virtual frequencies in all the ve [M(CO)8] (M, the molecular orbitals with the |ONs| of 1.98, which is q = Ca, 2−; Sc, 1−; Ti, 0; V, 1+; Cr, 2+) complex or ions.The contributed by the ligands entirely because all the nine valence fi q vibrational frequencies of ve M (CO)8 are listed in the AOs of Ti are composed of the nine MOs including seven Supplementary Information (Supplementary Table 1). Because σ-orbitals and two d → π* orbitals.

COMMUNICATIONS CHEMISTRY | (2020)3:39 | https://doi.org/10.1038/s42004-020-0285-2 | www.nature.com/commschem 3 ARTICLE COMMUNICATIONS CHEMISTRY | https://doi.org/10.1038/s42004-020-0285-2

q Fig. 2 AdNDP analyses of metal−ligand bonds. a AdNDP analyses of [M(CO)8] (M, q = Ca, 2−; Sc, 1−; Ti, 0; V, 1+; Cr, 2+) complex/ions. b The q detailed AdNDP analyses of (|ONs|) of the ﬁve M (CO)8 complex/ions with the participation of a2u orbital. c The detailed AdNDP analyses of (|ONs|) of q q the ﬁve M (CO)8 complex/ions without the participation of a2u orbital. d The occupied numbers (|ONs|) of M (CO)8 complex/ions with/without the participation of a2u orbital.

q Table 1 The results of AdNDP analysis and occupied numbers of [M(CO)8] (M, q = Ca, 2−; Sc, 1−; Ti, 0; V, 1+; Cr, 2+).

AdNDP analysis Orbital type Occupied numbers (|ONs|) of orbitals

2− − + 2− [Ca(CO)8] [Sc(CO)8] Ti(CO)8 [V(CO)8] [Cr(CO)8] Localized MOs of CO 8 × LP(O) LPs on O atom 1.98|e| 1.98|e| 1.97|e| 2.00|e| 1.98|e| 16 × π(CO) π-type bonds of CO 2.00|e| 1.99|e| 2.00|e| 2.00|e| 2.00|e| (C: 0.47, (C: 0.49, (C: 0.52, (C: 0.59, (C: 0.47, O: 1.53) O: 1.50) O: 1.48) O: 1.41) O: 1.53) 8×σ(CO) σ-type bond of CO 2.00|e| 2.00|e| 2.00|e| 2.00|e| 2.00|e| (C: 0.56, (C: 0.57, (C: 0.58, (C: 0.54, (C: 0.58, O: 1.44) O: 1.43) O: 1.42) O: 1.46) O: 1.42) Delocalized MOs 1 × 9c- S-type bond with a1g, 2.00|e| 2.00|e| 2.00|e| 2.00|e| 1.99|e| among ligands 2e bonds symmetry (C: 1.61, (C: 1.54, (C: 1.55, (C: 1.54, (C: 1.46, and metal Ca: 0.39 Sc: 0.43 Ti: 0.45) V: 0.46) Cr: 0.53) 3 × 9c- Px,Py and Pz bonds 1.99|e| 1.98|e| 1.97|e| 1.98|e| 1.99|e| 2e bonds with t1u, symmetry (C: 1.63, (C: 1.20, (C: 1.31, (C: 1.08, (C: 1.60, Ca: 0.36) Sc: 0.78) Ti: 0.46) V: 0.90) Cr: 0.39) 3 × 9c- Dxy,Dyz,Dzx bonds 1.99|e| 1.98|e| 1.98|e| 1.98|e| 1.98|e| 2e bonds with t2g, symmetry (C: 1.51, (C: 1.56, (C: 1.07, (C: 1.53, (C: 1.75, Ca: 0.48) Sc: 0.42) Ti: 0.91) V: 0.45) Cr: 0.23) 1 × 9c- F bond with a2u, 1.98|e| 1.98|e| 1.97|e|) 1.98|e|) 1.99|e|) 2e bonds symmetry (C: 1.98, (C: 1.98, (C: 1.97, (C: 1.98, (C: 1.99, Ca: 0) Sc: 0) Ti: 0) V: 0) Cr: 0) 2 × 17c- Dz2,Dx2−y2 bonds 2.00|e| 1.98|e| 2.00|e| 2.00|e| 2.00|e| 2e bonds with eg, symmetry (C: 1.12, (C: 0.85, (C: 0.58, (C: 0.32, (C: 0.17, O: 0.35, O: 0.29, O: 0.22, O: 0.12, O: 0.06, Ca: 0.53) Sc: 0.86) Ti: 1.20) V: 1.56) Cr: 1.77)

“ ” + + + The contribution of ligand-only a2u orbital. In order to make (a1g 3t1u 3t2g a2u) in forming eight coordinative bonds, q = − clear whether the a2u orbital in any [M(CO)8] (M, q Ca, 2 ; where C contributes 1.31|e| and Ti contributes 0.63|e| in each Sc, 1−; Ti, 0; V, 1+; Cr, 2+) participates in the formation of eight covalence bond. However, the |ONs| are decreased to 1.71|e| coordinative bonds, we apply the AdNDP method to compare the when we localize only a1g,3t1u and 3t2g orbitals in forming the |ONs| of eight Ti-C orbitals of Ti(CO)8 with and without the eight coordinative orbitals, where the component of C is participation of the a2u orbital (Fig. 2b, c). The |ONs| are 1.94|e| decreased from 1.31|e| to 1.08|e|. However, the |ONs| of Ti are with the contribution of a2u orbital if we localize eight orbitals still 0.63|e|, which equals to the value including the contribution

4 COMMUNICATIONS CHEMISTRY | (2020)3:39 | https://doi.org/10.1038/s42004-020-0285-2 | www.nature.com/commschem COMMUNICATIONS CHEMISTRY | https://doi.org/10.1038/s42004-020-0285-2 ARTICLE

2− − + of a2u orbital. This means the reduced |ONs| are caused by the to 1.72 (1.71/1.72/1.73) of [Ca(CO)8] ([Sc(CO)8] /[V(CO)8] / 2+ deduction of the a2u orbital contributed by the ligands, which [Cr(CO)8] ) suggests the a2u orbital contribute around 1/8 ﬁ q demonstrates the a2u orbital is still participating in the coordi- components in the coordinative orbital of the ve M (CO)8 nation, although it is contributed only by the ligands. systems (Table 2). For another aspect, the diminution of |ONs| from 1.94|e| to In order to make sure the ratio is 1:7 between bonding orbitals 1.71|e| suggests around 1/8 components (Table 2) of the and nonbonding orbitals, we further compare the bond popula- coordinative orbitals have been deducted, which is the contribution of Metal-C bond of “20-e” Ti(CO)8 (Oh symmetry) with the “ ” tion of the a2u orbital in the coordination. After dealing with a2u standard 18-e Ti(CO)7 (C3V symmetry), based on the results of q q 2− − + 23 24 orbitals of the other four M (CO)8 ions (M = Ca ,Sc ,V or Wiberg bond index (WBI) and Mayer bond order (MBO) Cr2+) (Fig. 2d) with the same methods, we also obtain similar calculations under the same theoretical level in Table 3. There are results. The diminution of |ONs| from 1.96 (1.94/1.95/1.96) exactly seven bonding orbitals in Ti(CO)7 with the bond order of 7 because there is no a2u orbital, which is different from Ti(CO)8 with the bond order of 7 but including 7 bonding orbitals and 1 Table 2 The contribution of the ligand-only a2u orbital in the nonbonding orbital. So the differences of the population are coordinative bond. caused by the “ligand-only” a2u orbital. The ratio of the Ti-C bond populations between Ti(CO)8 and Ti(CO)7 is the ratio of 2− − + 2+ [Ca(CO)8] [Sc(CO)8] Ti(CO)8 [V(CO)8] [Cr(CO)8] the bonding orbitals in Ti(CO)8. Therefore, it can be concluded |ONs|1 1.96 1.94 1.94 1.95 1.96 that the bonding orbitals occupy around 7/8ths (nonbonding |ONs|2 1.72 1.71 1.71 1.72 1.73 orbital contribute 1/8 components) in the coordination. The Ratio 12.2% 11.9% 11.8% 11.8% 11.7% q = similar comparisons for the other three [M(CO)8] ions (M, q − + + |ONs|1 is the occupation number including the contribution of a2u orbital. |ONs|2 is the Sc, 1 ;V,1; Cr, 2 ) are listed in the Supplementary occupation number without the contribution of a2u orbital. Information (Supplementary Table 3), where we can obtain Ratio is the components of the a orbital, which is calculated as: (|ONs|1 − |ONs|2)/|ONs|1. 2u similar conclusions. q So in the octacarbonyl metal complex or ions [M(CO)8] (M, q = Ca, 2−; Sc, 1−; Ti, 0; V, 1+; Cr, 2+; Ba, 2−), it is more reasonable to view the ligand-only a2u orbital as a nonbonding Table 3 The ratio of bonding orbitals in Ti(CO)8 by orbital contributes to form the eight coordinative orbitals population analysis of Ti(CO)7 and Ti(CO)8. 2 6 6 2 (a1g t1u t2g a2u ), where each coordinative bond contains 1/8 nonbonding orbitals and 7/8 bonding orbitals as shown in Fig. 3. Ti(CO)8 Ti(CO)7 Ratio Based on the MO theory, there are seven bonding orbitals WBI(Ti-C) 0.88 1.03 0.854/1 corresponding to the eight 7/8ths bonding orbitals, one MBO(Ti-C) 0.76 0.91 0.835/1 nonbonding orbital corresponding to the eight 1/8th nonbonding orbitals in forming the eight coordinative bonds. The eight *The ratio of the bonding orbital in Ti(CO) . 8 coordinative bonds with the bond order of 7 is consistent with the

q q Fig. 3 MO diagram of [M(CO)8] (M, q = Ca, 2−; Sc, 1−; Ti, 0; V, 1+; Cr, 2+; Ba, 2−). a The σ orbital diagram of [M(CO)8] . b The d−π* backdonation q q bonds of [M(CO)8] . c The conﬁguration as Jellium model by viewing M (CO)8 as a “20-e superatom”.

COMMUNICATIONS CHEMISTRY | (2020)3:39 | https://doi.org/10.1038/s42004-020-0285-2 | www.nature.com/commschem 5 ARTICLE COMMUNICATIONS CHEMISTRY | https://doi.org/10.1038/s42004-020-0285-2 results of both VB and HO theories. Furthermore, the 6. Zhao, L., Pan, S., Zhou, M. & Frenking, G. Response to Comment on “ = coordinative structures of the octacarbonyl metal complexes or Observation of alkaline earth complexes M(CO)8 (M Ca, Sr, or Ba) that “ ” fi mimic transition metals”. Science https://doi.org/10.1126/science.aay5021 (2019). ions can be viewed as a 20-e superatom with the con guration “ 2 6 10 2 7. Landis, C. R., Hughes, R. P. & Weinhold, F. Comment on Observation of of |1S |1P |1D |1 F | based on the unambiguous Jellium model. alkaline earth complexes M(CO) (M = Ca, Sr, or Ba) that mimic transition 10 8 In this model, |1D | orbitals split into two groups including the metals”. Science https://doi.org/10.1126/science.aay2355 (2019). σ 6 = three -type coordinative orbitals (|1D |) with lower energy and 8. Wu, X. et al. Observation of alkaline earth complexes M(CO)8 (M Ca, Sr, or two π-type backdonation orbitals (|1D4|) with higher energy. The Ba) that mimic transition metals. Science 361, 912–916 (2018). nonbonding orbital with a symmetry corresponds to |1F| super 9. Murrell, J. N., Kettle, S. F. A. & Tedder, J. M. The Chemical Bond 2nd edn 2u (London and New York, Wiley, 1985). orbital (1Fxyz) rather than the |2S| orbital, which is caused by the 10. Carey, F. A. Advanced Organic Chemistry 4−6 (Springer, 2001). splitting of 1F orbitals (Fig. 3c). 11. Davidson, E. R., Kunze, K. L., Machado, F. B. C. & Chakravorty, S. J. The This research demonstrates the Jellium model is a powerful transition metal-carbonyl bond. Acc. Chem. Res. 26, 628–635 (1993). analysis tool that can not only be applied on metal clusters but 12. Knight, W. D. et al. Electronic shell structure and abundances of sodium also be useful to understand the high symmetric octacarbonyl clusters. Phys. Rev. Lett. 52, 2141 (1984). 13. Heer, W. Ad The physics of simple metal clusters: experimental aspects and metal complexes or ions. The a2u orbital is indeed a ligand-only simple models. Rev. Mod. Phys. 65, 611 (1993). orbital but contributes 1/8 components in each coordinative 14. Liu, L., Yuan, J., Cheng, L. & Yang, J. New insights into the stability and q q = − – bonds in [M(CO)8] complex or ions [M(CO)8] (M, q Ca, 2 ; structural evolution of some gold nanoclusters. Nanoscale 9, 856 861 (2017). Sc, 1−; Ti, 0; V, 1+; Cr, 2+; Ba, 2−). Therefore, 20-e model with 15. Cheng, L. Quintuple super bonding between superatoms of metallic clusters. – the configuration |1S2|1P6|1D10|1F2| is an appropriate description Nanoscale 9, 13209 13213 (2017). 16. Chen, J., Luo, Z. & Yao, J. Theoretical study of tetrahydrofuran-stabilized of the valence bonding structures of M(CO)8 or TM(CO)8 Al13 superatom cluster. J. Phys. Chem. A 120, 3950–3957 (2016). complexes and ions. 17. Bergeron, D. E., Castleman, A. W., Morisato, T. & Khanna, S. N. Formation of − – Al13 : evidence for the superhalogen character of Al13. Science 304,84 87 Methods (2004). Optimization. On the basis of the synthesized octacarbonyl alkali earth metal 18. Bergeron, D. E., Roach, P. J., Castleman, A. W., Jones, N. O. & Khanna, S. N. q = − Al cluster superatoms as halogens in polyhalides and as alkaline earths in complexes, we have designed six [M(CO)8] complex or ions (M, q Ca, 2 ; − + + − 2− iodide salts. Science 307, 231–235 (2005). Sc, 1 ; Ti, 0; V, 1 ; Cr, 2 ; Ba, 2 ) and a metal cluster [BaBe8] . All the structures are optimized at M06-2×/def2tzvpp level of theory19,20 in Gaussian 19. Weigend, F. & Ahlrichs, R. Balanced basis sets of split valence, triple zeta 09 (Version E. 01)21 to obtain their singlet electronic ground states. All the valence and quadruple zeta valence quality for H to Rn: Design and – structures with the coordination information are listed in the Supplementary assessment of accuracy. Phys. Chem. Chem. Phys. 7, 3297 3305 (2005). Information (Supplementary Figs. 2–12 and Supplementary Tables 4–14). 20. Zhao, Y. & Truhlar, D. G. The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of Analysis of structural stability. Based on the optimized structures, we calculated four M06-class functionals and 12 other functionals. Theor. Chem. Acc. 120, the vibrational frequencies (cm−1) and HOMO-LUMO gaps (eV) under M06-2×/ 215–241 (2008). def2tzvpp theoretical level. Because we did not find the stable conformation of [Ca 2− q → 21. Frisch, M. J. T., et al. Gaussian 09 (Gaussian, Inc., Wallingford CT, 2009). (CO)7] , we only calculated the corresponding dissociation energies of [M(CO)8] − + + 22. Zubarev, D. & Boldyrev, A. Developing paradigms of chemical bonding: adaptive [M(CO) ]q + CO for [Sc(CO) ] , [Ti(CO) ], [V(CO) ] and [Cr(CO) ]2 .Allthe 7 8 8 8 8 natural density partitioning. Phys. Chem. Chem. Phys. 10, 1463–9076 (2008). structures are optimized under the same theoretical methods. The dissociation energy is the Gibbs free energy variation of the corresponding reaction. All the results are 23. Wiberg, K. B. Application of the pople-santry-segal CNDO method to the listed in Supplementary Tables 1 and 2. cyclopropylcarbinyl and cyclobutyl cation and to bicyclobutane. Tetrahedron 24, 1083–1096 (1968). 24. Mayer, I. Charge, bond order and valence in the AB initio SCF theory. Chem. Analysis of MOs. With the same methods, each orbital contributed by both ligand Phys. Lett. 97, 270–274 (1983). and center metal has been manipulated with structural subunits of Metal-C bonds, 25. Varetto, U. MOLEKEL 5.4 (Swiss National Supercomputing Centre, Manno, fi 22 which is con rmed by the NBO analysis by using the AdNDP method .MO Switzerland, 2009). 25 visualization is performed using MOLEKEL 5.4 software . On the basis of opti- 26. Lu, T. & Chen, F. Multiwfn: a multifunctional wavefunction analyzer. J. mized structures, the WBI has been obtained directly from Gaussian 09 program Comput. Chem. 33, 580–592 (2012). by using NBO population analysis. The MBO is obtained by using Multiwfn tools (Version 3.6)26. Acknowledgements Data availability This work is financed by the National Natural Science Foundation of China (21701001, The data that support the findings of this study are available from the corresponding 21873001) and by the Foundation of Distinguished Young Scientists of Anhui Province. authors upon reasonable request. The calculations are carried out at the High-Performance Computing Center of Anhui University. Received: 29 November 2019; Accepted: 21 February 2020; Author contributions Published online: 26 March 2020 K.W. performed the analysis and wrote the manuscript. K.W. and L.C. designed the models and conceived the project. K.W., C.X, D.L. and L.C. performed the structure optimization and AdNDP analysis. L.C. supervised the project.

References Competing interests 1. Frenking, G. & Fröhlich, N. The nature of the bonding in transition-metal The authors declare no competing interests. compounds. Chem. Rev. 100, 717–774 (2000). 2. Leigh, G. J. & Winterton, N. Modern Coordination Chemistry: The Legacy of Joseph Chatt 111 (The Royal Society, 2002). Additional information 3. Jin, J. et al. Octacarbonyl anion complexes of group three transition metals Supplementary information is available for this paper at https://doi.org/10.1038/s42004- [TM(CO)8]@ (TM = Sc, Y, La) and the 18-electron rule. Angew. Chem. Int. 020-0285-2. Ed. 57, 6236–6241 (2018). 4. Xing, X. et al. Octacoordinate metal carbonyls of scandium and yttrium: Correspondence and requests for materials should be addressed to L.C. theoretical calculations and experimental observation. Rapid Commun. Mass Spectrom. 27, 1403–1409 (2013). Reprints and permission information is available at http://www.nature.com/reprints 5. Luo, Q. et al. Bonding of seven carbonyl groups to a single metal atom: = = theoretical study of M(CO)n (M Ti, Zr, Hf; n 7, 6, 5, 4). J. Am. Chem. Soc. Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in 130, 7756–7765 (2008). published maps and institutional afﬁliations.

6 COMMUNICATIONS CHEMISTRY | (2020)3:39 | https://doi.org/10.1038/s42004-020-0285-2 | www.nature.com/commschem COMMUNICATIONS CHEMISTRY | https://doi.org/10.1038/s42004-020-0285-2 ARTICLE

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/ licenses/by/4.0/.

COMMUNICATIONS CHEMISTRY | (2020)3:39 | https://doi.org/10.1038/s42004-020-0285-2 | www.nature.com/commschem 7